Question

there is a right triangle in the figure, with a right angle, one angle is 47°, the hypotenuse is 17, and the other two sides are a and b. there are three blanks to fill: angle a, side a, side b.

Explanation:

Step1: Calculate angle $A$

Sum of angles in triangle: $180^\circ - 90^\circ - 47^\circ = 43^\circ$

Step2: Calculate side $a$

Use sine: $a = 17 \sin(47^\circ) \approx 17 \times 0.7314 \approx 12.5$

Step3: Calculate side $b$

Use cosine: $b = 17 \cos(47^\circ) \approx 17 \times 0.6820 \approx 11.6$

Answer:

$A = 43^\circ$, $a \approx 12.5$, $b \approx 11.6$